Finite Group Databasebeta

← #29580633

Subgroups — #29580633

Order 15616.

518 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455763C211yesmaximal, characteristic, complemented
2#21455755C211yesmaximal, characteristic
3#21445888C211yesmaximal, characteristic, complemented
4#21444183C211yesmaximal, characteristic, complemented
5#21444179C211yesmaximal, characteristic
6#21443696C211yesmaximal, characteristic, complemented
7C61×#3187C211yesmaximal, characteristic
8C2×#14519736C2211yescharacteristic
9#16840100—22no—
10#16840095—21no—
11#16840090—21no—
12#16840083—22no—
13#16840078—21no—
14#16840073—21no—
15#16839802—21no—
16#16839802—21no—
17#16839771—21no—
18#16839767—21no—
19#16839726C2211yescharacteristic
20#16839726C2211yescharacteristic
21C2×C22⋊#92418C2211yescharacteristic
22#16839516—22no—
23#16839488—22no—
24#16839486—22no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C61×#483—21no—
28C61×#481—21no—
29C61×#465—22no—
30C61×#450—21no—
31C61×#448—21no—
32C2×C22⋊C8×C61C2211yescharacteristic
33C2×#11758194—21no—
34C2×#11758194—21no—
35C22×#92418—21no—
36#14519736—21no—
37#14519736—21no—
38#14519736—21no—
39#14519736—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C4×Dic61—21no—
44#14519710—22no—
45#14519710—22no—
46#14519708—22no—
47#14519708—22no—
48#14519701—22no—
49#14519701—22no—
50#14519698—22no—
51#14519698—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C22⋊#92418D412yes—
57C22⋊#92418D412yes—
58C22×Q8×C61D411yescharacteristic
59C22×D4×C61—21no—
60C22×D4×C61D411yescharacteristic
61C23×C4×C61C2311yescharacteristic
62C2×SD16×C61—22no—
63C22×C8×C61D412yes—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68#121×C61—21no—
69#121×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77#106×C61—22no—
78#103×C61—22no—
79#102×C61—22no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61—21no—
82C24×C61—21no—
83C24×C61#4111yescharacteristic
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—42no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—42no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—82no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—42no—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×Dic61—21no—
104C22×Dic61—21no—
105SD16×C61—82no—
106C2×C8×C61—22no—
107C2×C8×C61—42no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊Dic61—41no—
119C22⋊Dic61—41no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4×Dic61—41no—
125C4×Dic61—41no—
126#11758194—42no—
127#11758194—42no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—42no—
131C2×#92418—41no—
132C23×C61—22no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—42no—
136C23×C61—41no—
137C23×C61—81no—
138C23×C61—81no—
139C23×C61#12111yescharacteristic
140C23×C61#12111yescharacteristic
141C23×C61#12111yescharacteristic
142Q8×C61—42no—
143Q8×C61—42no—
144D4×C61—42no—
145D4×C61—42no—
146D4×C61—82no—
147D4×C61—82no—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61#12011yescharacteristic
161C2×C4×C61#12011yescharacteristic
162C2×C4×C61#12011yescharacteristic
163C2×C4×C61#12711yescharacteristic
164C2×Dic61—42no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C8×C61—42no—
169#92418—42no—
170#92418—42no—
171#92418—81no—
172#9978—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—82no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—162no—
186C22×C61#39211yescharacteristic
187C22×C61#47112yes—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—81no—
192C4×C61—81no—
193C4×C61—81no—
194C4×C61#45812yes—
195Dic61—81no—
196Dic61—81no—
197#3187D6111yescharacteristic
198#3095—611no—
199#3094—611no—
200#1818—611no—
201#1472—611no—
202#1471—611no—
203#1293—611no—
204C2×C61—22no—
205C2×C61—41no—
206C2×C61—41no—
207C2×C61—161no—
208C2×C61#201711yescharacteristic
209C2×C61#201911yescharacteristic
210C2×C61#202211yescharacteristic
211C2×C22⋊Q8C2×D6111yescharacteristic
212C2×#121C2×D6111yescharacteristic
213C2×#117—611no—
214#485—1222no—
215#484—1221no—
216#483—21no—
217#483—1221no—
218#482—1222no—
219#481—21no—
220#481—1221no—
221#480—1221no—
222#465—22no—
223#450—21no—
224#448—21no—
225#428—1221no—
226#428—1221no—
227#419—1221no—
228#418—1221no—
229#407—611no—
230#407—611no—
231C2×C22⋊C8—611no—
232C2×C22⋊C8C2×D6111yescharacteristic
233#336—1222no—
234#324—1222no—
235#323—1222no—
236C61#997811yescharacteristic, complemented, Sylow
237C22×Q8C22⋊D6111yescharacteristic
238C22×D4—21no—
239C22×D4C22⋊D6111yescharacteristic
240C23×C4C22×D6111yescharacteristic
241C2×SD16—22no—
242C2×M16—1221no—
243C2×M16—1221no—
244C22×C8—1221no—
245C22×C8C22⋊D6112yes—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250#121—21no—
251#121—21no—
252#121—21no—
253#121—21no—
254#117—1221no—
255#117—1221no—
256#117—1221no—
257#117—1221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4C22⋊D6111yescharacteristic
262C2×C4⋊C4C22⋊D6111yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—1221no—
266C2×C42—1221no—
267#107—1222no—
268#107—1222no—
269#106—22no—
270#106—1222no—
271#106—1222no—
272#103—22no—
273#103—1222no—
274#103—1222no—
275#102—22no—
276#102—1222no—
277#102—1222no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—612no—
281C22⋊C8—612no—
282C22⋊C8—1221no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286C24—21no—
287C24#1175822411yescharacteristic
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—42no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—82no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4D4×D6111yescharacteristic
304C22×C4D4×D6111yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4C2×C22⋊D6111yescharacteristic
307C22×C4C2×C22⋊D6111yescharacteristic
308C22×C4C2×C22⋊D6111yescharacteristic
309SD16—82no—
310M16—2442no—
311M16—2442no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—1222no—
315C2×C8—1222no—
316C2×C8—2442no—
317C2×C8—2441no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C42—2441no—
335C42—2441no—
336C23—22no—
337C23—41no—
338C23—41no—
339C23—42no—
340C23—41no—
341C23—81no—
342C23—81no—
343C23#1451974811yescharacteristic
344C23#1451974911yescharacteristic
345C23#1451974911yescharacteristic
346Q8—42no—
347Q8—42no—
348D4—42no—
349D4—42no—
350D4—82no—
351D4—82no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—2442no—
365C2×C4—2442no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4#1451974511yescharacteristic
369C2×C4#1451974511yescharacteristic
370C2×C4#1451974611yescharacteristic
371C2×C4#1451977311yescharacteristic
372C8—42no—
373C8—4881no—
374C8—2442no—
375C8—2442no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—82no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—162no—
389C22#1683967011yescharacteristic
390C22#1684002212yes—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—4881no—
398C4—4881no—
399C4#1683995212yes—
400C2—22no—
401C2—41no—
402C2—41no—
403C2—161no—
404C2#2144692211yescharacteristic
405C2#2144693111yescharacteristic
406C2#2144694811yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#3187C2
socleC22×C61#392
prime radicalC2×#121×C61C22
hypercenter#3187D61
hypocenterC61#9978
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21455763C2semidirect
3. #21445888C2semidirect
4. #21444183C2semidirect
6. #21443696C2semidirect
236. C61#9978semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214557632
#214557552
#214458882
#214441832
#214441792
#214436962
C61×#31872
#997861